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Question : If $a+\frac{1}{a-2}=4$, then the value of $(a-2)^{2}+(\frac{1}{a-2})^{2}$ is:
Option 1: 0
Option 2: 2
Option 3: –2
Option 4: 4
Correct Answer: 2
Solution : Given: $a+\frac{1}{a-2}=4$ Subtracting 2 from both sides, ⇒ $a-2+\frac{1}{a-2}=2$ Squaring both sides, ⇒ $( a-2)^2+\frac{1}{( a-2)^2} + 2=2^2$ ⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2^2-2$ ⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2$ Hence, the correct answer is 2.
Question : The mahogany tree is found in which of the following types of vegetation?
Option 1: Mangrove forests
Option 2: Tropical evergreen forests
Option 3: Tropical thorn forests
Option 4: Montane forests
Correct Answer: Tropical evergreen forests
Solution : The correct answer is Tropical evergreen forests
Tropical evergreen forests are prevalent in areas characterised by consistently high temperatures and abundant rainfall. These ecosystems, often referred to as rainforests, support a diverse array of plant and animal life. Among the notable flora found
Question : The Rourkela steel plant was set up in collaboration with Germany in which the state of India?
Option 1: Jharkhand
Option 2: Bihar
Option 3: Assam
Option 4: Odisha
Correct Answer: Odisha
Solution : The correct option is Odisha.
One of India's biggest steel production sites is the Rourkela Steel Plant. It is located in the city of Rourkela in the Sundargarh district of Odisha. One of India's earliest integrated steel factories, the Rourkela Steel Plant was founded in
Question : In a 1500 m race, Anil beats Bakul by 150 m, and in the same race, Bakul beats Charles by 75 m. By what distance does Anil beat Charles?
Option 1: 217.50 m
Option 2: 200.15 m
Option 3: 293.50 m
Option 4: 313.75 m
Correct Answer: 217.50 m
Solution : In 1500 m race, Anil beats Bakul by 150 m. When Anil completes the race, Bakul covers 1500 – 150 = 1350 m Bakul beats Charles by 75 m in 1500 m race. So in a 1350 m race, Bakul is ahead of Charles
Question : P can fill a tank in 5 hours, and Q can fill the same tank in 10 hours. R can empty the same tank in 20 hours. How much time will all the three take together to fill the same tank?
Option 1: 10 hours
Option 2: 4 hours
Option 3: 6 hours
Option 4: 5 hours
Correct Answer: 4 hours
Solution : P can fill a tank in 5 hours. Q can fill the same tank in 10 hours. R can empty the same tank in 20 hours. P's per hour efficiency = $\frac{1}{5}$ Q's per hour efficiency = $\frac{1}{10}$ R's per hour efficiency = $-
Question : Select the correct passive form of the given sentence.
May you achieve success in all your endeavours.
Option 1: May success will be achieved by you in all your endeavours.
Option 2: Success might be achieved by you in all your endeavours.
Option 3: May success be achieved by you in all your endeavours.
Option 4: Success has been achieved by you in all your endeavours.
Correct Answer: May success be achieved by you in all your endeavours.
Solution : The correct choice is the third option.
Explanation: In a passive voice construction, the subject of the sentence receives the action, and the focus is on the action rather than the doer. The verb "achieve" becomes
Question : If $4x^2-12x+k$ is a perfect square, then the value of $k$ is:
Option 1: 2
Option 2: 9
Option 3: 12
Option 4: 10
Correct Answer: 9
Solution : Given: $4x^2-12x+k$ is a perfect square. $4x^2-12x+k=(2x)^2-2×2x×3+k$ Since this a perfect, So, $(2x)^2-2×2x×3+k=(2x)^2-2×2x×3+3^2=(2x–3)^2$ Value of $k$ is 32 = 9 Hence, the correct answer is 9.
Question : Select the most appropriate meaning of the given idiom.
To eat crow
Option 1: To take great care
Option 2: To become non-vegetarian
Option 3: To take money back
Option 4: To admit that one is wrong
Correct Answer: To admit that one is wrong
Solution : The correct choice is the fourth option.
Explanation: To eat crow originated from a time when eating a crow (a scavenging bird) was considered a humiliating act. So, figuratively, it means admitting a mistake or being forced to accept
Question : Mr Dutta desired to deposit his retirement benefit of 3 lakh partly to a post office and partly to a bank at 10% and 6% simple interests respectively. If his monthly interest was Rs. 2,000, then the difference between his deposits in the post office and the bank was:
Option 1: Rs. 50,000
Option 2: Rs. 40,000
Option 3: Nil
Option 4: Rs. 1,00,000
Correct Answer: Nil
Solution : Let the amount deposited in the bank and post office be Rs. $x$ and Rs. $(300000-x)$ respectively. We know, interest = $\frac{PRT}{100}$, where $P$ is principal, and $R$ is the rate of interest per annum for $T$ years. So, Interest gained from a 10% interest
Question : Which among the following rocks may contain fossils of plants, animals and other microorganisms that once lived on them?
Option 1: Metamorphic rocks
Option 2: Intrusive igneous rocks
Option 3: Sedimentary rocks
Option 4: Extrusive igneous rocks
Correct Answer: Sedimentary rocks
Solution : The correct option is Sedimentary rocks.
The type of rock that may contain fossils of plants, animals, and other microorganisms that once lived on or in them is called sedimentary rock. Sedimentary rocks are formed from the accumulation and cementation of sediments, which
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